The goal of this project is to develop improved statistical methods for toxicology and laboratory studies. Work has proceeded in three areas: (1) the development of methods for analysis of multiple outcome data in 2-year bioassays, transgenic mouse studies, and other experiments with related measures of an underlying health condition; (2) the development of methods to improve efficiency and power through the incorporation of order restrictions (for example, non-decreasing dose response); and (3) the development of more flexible and biologically-motivated models, which allow animal-specific susceptibility and other "latent variables" to change flexibly with age and other factors. In the first area, we have made substantial progress, developing a new modeling framework for analysis of multiple discrete outcomes. We applied this framework to assess joint effects of chemical exposures of tumor latency, multiplicity, and malignancy in transgenic mouse bioassays, but the method can be used broadly for joint analysis of different types of discrete outcomes. In the second area, we developed an approach for multivariate isotonic regression and applied this approach to multi-site tumor data from bioassay studies. In particular, we assessed the joint effect of body weight on tumor incidence in different organ sites. In the third area, we developed a flexible statistical modeling framework, which allows the distribution of susceptibility to vary in unanticipated ways across animals and over time. This framework improves upon standard shared "frailty models", which require susceptibility to have a known distribution that is constant with age. This improved flexibility allows researchers to study changes in the susceptibility distribution with age, and to identify outlying subjects for further examination.